The use of large tonnage thermoforming frames and drive mechanisms is known where pneumatic pressure is being applied to a heated sheet of thermoformable material during an article forming operation. Where large arrays of articles are provided on die plates on a platen, the surface area subject to pneumatic pressure and/or vacuum generates very large loads on the kinematic drive linkages and frame of a thermoforming machine. Improvements are needed in order to enable forming using very large loads without requiring further increases in the size and strength of traditional frames and linkages of a thermoforming machine, particularly when forming newer plastic sheet materials and/or article geometries that require greater forming pressures and loads.